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Entropy
Entropy is a well-known measure of disorder or unavailability of energy in a (closed) system. More entropy generally means less predictability, hence one often tries to minimize it. Instead of plagiarizing or copying information to this page, I recommend the reader to take a look at the excellent math site (www.mathworld.com), and particularly to the definition of Entropy. Entropy has a different meaning in maths and physics, and many different measures have been devised in the literature.
The Maximum Entropy Method is one way to enhance the signal-to-noise ratio in data. There is ample information and even software available (cf. MESA). We would recommend the NtropiX site from John Conover, from which we have designed a simple Entropy indicator for NeuroShell Trader. John Conover's site also includes a Excel spreadsheet calculating entropy. We have implemented our own flavour for TradeStation in our toolset (http://ts-trading-technique.blogspot.com)
Here is a sample chart showing our earlier Entropy indicator for NeuroShell Trader:
The source C code for this indicator is quite simple and is here provided for NeuroShell Trader, which can be compiled with any (free) C compiler:
#include "math.h"
#include "stdlib.h"
__declspec(dllexport) void Entropy (double *price, double *entropy, long int
size, long int numbars)
{
double *in, *out, P, G;
long int i,j;
double sumx = 0.0;
double sumx2 = 0.0;
double avgx = 0.0;
double rmsx = 0.0;
in=price;
out=entropy;
for (i=0; i<size; i++)
{
if (i < numbars+1) *out = 3.4e38;
else
{
sumx = sumx2 = avgx = rmsx = 0.0;
for (j=0;j<numbars+1;j++)
{
sumx += log(*(in-j) / *(in-j-1)) ;
sumx2 += log(*(in-j) / *(in-j-1)) * log(*(in-j) / *(in-j-1));
}
if (numbars==0)
{
avgx = *in;
rmsx = 0.0;
}
else
{
avgx = sumx / numbars;
rmsx = sqrt(sumx2/numbars);
}
P = ((avgx/rmsx)+1)/2.0;
G = P * log(1+rmsx) + (1-P) * log(1-rmsx);
*out=G;
}
in++; out++;
}
}
It can easily be called from within NeuroShell Trader (4 parameters: input,
output, size, numbars).